Question: Use the triangle law of vector addition to derive the following relationships between the unit polar basis and the standard cartesian basis.
Er=cos(theta)i+sin(theta)j
i=cos(theta)er-sin(theta)e(theta)
(there's two other relations but you know what they are, it would get too messy to write them)
I have drawn some diagrams but I'm not sure how to write the proof exactly...
Any ideas would be appreciated!
Hey Plato
Here's a picture of the problem; it might clarify what is meant by the unit polar basis. It's problem number 6.
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I would assume it means a 2 dimensional basis where the first vector is "r" and the second "theta", and each is a unit vector.
Thanks for any help!
this doesn't quite make sense: 'first vector is "r" and the second "theta"' because those are numbers, not vectors. I think what you mean rather is that we have different basis vectors at each point. One of the basis vectors, , at (x, y), is the unit vector whose direction is away from the origin, along the line y= x, and the other, is the unit vector perpendicular to that in the direction of increasing angle. Those. I presume, are your "er" and "e(theta)", respectively.
But I don't know what you mean by "Er" and "i"? did you mean "er" again? And is "i" the unit vector in the x-direction?